Finite-Source Effects and Transit Chords: What the Source-Size Parameter Reveals About Lens Geometry

This paper computes what happens when the source star is no longer well treated as a point, and how the crossing time of its own angular radius measures the Einstein radius directly. For a representative lens of 0.3 solar masses at 6.0 kiloparsecs, in front of a source at 8.0 kiloparsecs, the angular Einstein radius is 0.319 milliarcseconds, the event timescale is 19.4 days at a relative proper motion of 6.0 milliarcseconds per year, the microlensing parallax is 0.131, and the physical Einstein radius projected at the lens is 1.91 astronomical units. The central finding is that a finite-source crossing measures the angular Einstein radius without any assumption about lens mass or distance, which is why such events carry disproportionate weight. All quantities are computed from stated assumptions and published survey values used as comparison points; the study is simulated and computed, not measured. Where the computation shows that an inference commonly drawn from such events is not supported at the stated precision, that negative result is reported in full.